Question

Intro It is the end of 2019. You (foolishly) played the lottery and won the following cash flows, to be paid at the end of each year:

Year 2020 2021 2022 2023 2024

Cash flow 1,300 1,600 1,800 2,000 2,200

The appropriate interest rate is 11%.

What is the sum of present values?

Now assume that the interest rate is 9%. What is the present value of all cash flows?

Now assume that the interest rate is 15%. What is the present value of all cash flows?

Answer 1

Present Value of the cash flows if the interest rate is 11%

Year	Annual Cash Flow ($)	Present Value factor at 11%	Present Value of Cash Flow ($)
2020	1,300	0.900901	1,171.17
2021	1,600	0.811622	1,298.60
2022	1,800	0.731191	1,316.14
2023	2,000	0.658731	1,317.46
2024	2,200	0.593451	1,305.59
TOTAL			6,408.97

Present Value of the cash flows will be $6,408.97

Present Value of the cash flows if the interest rate is 9%

Year	Annual Cash Flow ($)	Present Value factor at 9%	Present Value of Cash Flow ($)
2020	1,300	0.917431	1,192.66
2021	1,600	0.841680	1,346.69
2022	1,800	0.772183	1,389.93
2023	2,000	0.708425	1,416.85
2024	2,200	0.649931	1,429.85
TOTAL			6,775.98

Present Value of the cash flows will be $6,775.98.

Present Value of the cash flows if the interest rate is 15%

Year	Annual Cash Flow ($)	Present Value factor at 15%	Present Value of Cash Flow ($)
2020	1,300	0.869565	1,130.43
2021	1,600	0.756144	1,209.83
2022	1,800	0.657516	1,183.53
2023	2,000	0.571753	1,143.51
2024	2,200	0.497177	1,093.79
TOTAL			5,761.09

Present Value of the cash flows will be $5,761.09.

NOTE    

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.